President Obama and a divided Congress kick off a week of jockeying over the federal budget as House Republicans and Senate Democrats unveil competing fiscal blueprints and the president heads to Capitol Hill to continue his personal campaign for compromise.

The president spent part of Monday prepping for three trips to Capitol Hill over the next three days for closed-door meetings with House and Senate lawmakers in both parties. Obama is seeking an alternative to the sequestration, a $1.2 trillion across-the-board spending cut over the next decade that kicked in March 1 after Congress failed to find a better alternative to cut spending.

White House spokesman Jay Carney said the president will also urge Congress to use the budget process underway to reduce the deficit. “Our focus now, as the president has said, is on working with Congress in regular order on the budget process, and through that process hopefully produce a bipartisan agreement on deficit reduction,” Carney said.

The challenge of finding compromise between the two polarized parties will be underscored as House Budget Chairman Paul Ryan, R-Wis., and Senate Budget Chairwoman Patty Murray, D-Wash., unveil their parties’ budgets Tuesday and Wednesday, respectively.

Ryan, a potential 2016 presidential contender, has said the GOP budget will achieve balance in 10 years without raising taxes. It is also expected to include his proposal to overhaul Medicare from a guaranteed benefit to a premium support system where seniors receive federal subsidies to buy health care on the private market.

Democrats are again maneuvering to use the GOP Medicare overhaul as a political liability in 2014 — attacks they used in 2012 as well. The Senate Democratic campaign operation said Monday they would use the policies in the Ryan budget to target Senate candidates, highlighting 14 House Republicans who are either declared Senate candidates or mulling runs.

Republicans are likewise plotting to use the Senate Democrats’ budget — the first in three years — as political fodder in 2014. Their blueprint is expected to outline proposals to raise more revenues by closing tax loopholes.

“Democrats up for election in 2014 will be forced to defend a budget that features massive tax hikes, reckless spending and more debt while ignoring a Medicare crisis that even President Obama admits can’t be solved by raising taxes,” said Brad Dayspring, a spokesman for the Senate GOP’s campaign outfit.

The two chambers are unlikely to resolve the differences in the competing partisan budgets, but lawmakers are still working a parallel legislative track to find a more targeted path to deficit reduction than the sequester.

To mitigate the cuts’ effects, the House last week passed a spending bill to give the Pentagon more flexibility to implement the cuts. The Senate is on track this week to vote on a bill to extend that flexibility to domestic programs. If the two chambers can reconcile the differences before March 27, it will head off a government shutdown.

The president wants to replace the cuts entirely with an agreement that includes both spending cuts and new tax revenues, but Republicans oppose any additional tax increases beyond the $620 billion included in the January deal to avert the “fiscal cliff.”

Sen. Tammy Baldwin, D-Wis., who sits on the budget panel, said she is still confident that a long-term bipartisan agreement can be reached despite ongoing divides. “It’s going to take a little while, but there are a lot of pressures that could lead us in that direction,” Baldwin said in an interview with USA Today’s “Capital Download” on Monday.

“I do think that as this plays out in the months ahead, we have a real opportunity to at least stop living from fiscal crisis to fiscal crisis, cliff to cliff, if you will, which is something that has been very frustrating to the American people,” she said.